Question

How to construct the angle $75°$ ?

Answer 1

Step 1 Draw a ray and a Semicircular arc.

• Draw a ray $AB$ of any length with $A$ as fixed end.

• With $A$ as the center and any radius, draw an arc that cuts $AB$ at $C$ .

Step 2: Draw two arcs intersecting the Semicircular arc.

• With $C$ as the center and the same radius, draw an arc cutting the Semicircular arc at $D$. $D$ is at $60°$.

• With the same radius and with $D$ as center, draw an arc that cuts the Semicircular arc at $E$. $E$ is at $120°$.

Step 3: Draw the angle bisector of $E$ and $D$.

• With $E$ and $D$ as centers and with the same radius, draw two arcs cutting each other at $F$. $F$ is at $90°$.

• Join $AF$ , mark the point as $G$ where the line segment $AF$ intersects the semicircular arc .

Step 4: Draw the angle bisector of $F$ and $D$ that will be $75°$.

• Now with $G$ and $D$ as centers and the same radius, draw two arcs again cutting each other at $H$. $H$ is at $75°$.

Hence $\angle \mathrm{HAB}$ is the required $75°$ angle.